DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 46)

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Problem 1 :

The table above shows the distribution of test scores in Mrs. Keaton's class. Which of the following sets of test scores, if added would change the standard deviation of the distribution the least?

Solution :

Problem 2 :

The table shows three values of x and their corresponding values of g(x), where

and f is a linear function. What is the y-intercept of the graph of y = f(x) in the xy-plane?

A) (0, 36)

B) (0, 12)

C) (0, 4)

D) (0, -9)

Solution :

Problem 3 :

A machine launches a softball from ground level. The softball reaches a maximum height of 51.84 meters above the ground at 1.8 seconds and hits the ground at 3.6 seconds. Which equation represents the height above ground h, in meters, of the softball t seconds after it is launched?

A) h = -t² + 3.6

B) h = -t² + 51.84

C) h = -16(t – 1.8)² + 3.6

D) h = -16(t – 1.8)² + 51.84

Solution :

Problem 4 :

During a 5-second time interval, the average acceleration a, in meters per second squared, of an object with an initial velocity 12 meters per second is defined by the equation

where v_f is the final velocity of the object in meters per second. If the equation is reqritten in the form

v_f = xa + y

where x and y are constants, what is the value of x?

Solution :

Problem 5 :

x - y = 1

x + y = x² - 3

Which ordered pair is a solution to the system of equations above?

A) (1 + √3, √3)

B) (√3, -√3)

C) (1 + √5, √5)

D) (√5, -1 + √5)

Solution :

Problem 6 :

If x² + kx + k + 1 = (x + p)(x + 2) for all values of x. If k and p are constants, what is the value of k?

A) 5

B) 4

C) 3

D) 2

Solution :

Problem 7 :

f(x) = 2x² - 3

A) 3

B) 4

C) 5

D) 6

Solution :

Problem 8 :

In the xy-pane above, what is the measure, in radians, of angle AOB?

A) π/3

B) π/2

C) 5π/12

D) 7π/12

Solution :

Problem 9 :

In the xy-plane above, the figure shows a regular hexagon with side length of 5. What is the value of a?

A) 10.5

B) 11

C) 11.5

D) 12

Solution :

Problem 10 :

y > -2x + a

y < 3x + b

In the system of inequalities, a and b are constants. In the xy-plane, if (0, 1) is a solution to the system. Which of the following must be true?

A) a > b

B) a = b

C) a < b

D) a = -b

Solution :

Problem 11 :

The graph of y = x² – 8x + 16 is shown in the xy-plane above. If point P is the y-intercept of the graph, what is the area of rectangle OPQR?

Solution :

Problem 12 :

The cost C for maintenance on a heating system increases each year by 2.8%. If Mark paid $250 this year for maintenance, the cost t years from now can be given by the function C(t) = 250P^t. What is the approximate cost in 4 years?

A) $265

B) $279

C) $310

D) $320

Solution :

Problem 13 :

The graph of y = √3x is shown in the xy-plane above. What is the measure, in radians, of angle POR?

A) π/6

B) π/4

C) π/3

D) π/2

Solution :

Problem 14 :

In the equation above, what is the value of k?

A) 4

B) 5

C) 6

D) 7

Solution :

Problem 15 :

Claie works one week and earns a dollars. If she had worked 5 more hours, show would have earned b dollars. If the hourly rate is constant, what is the hourly rate?

A) b/5 dollars

B) a/5 dollars

C) (a - b)/5 dollars

D) (b - a)/5 dollars

Solution :

Problem 16 :

Which of the following is equivalent to the expression above?

Solution :

Problem 17 :

The function f(x) = x⁴ - 6x² - 4 is graphed in the xy-plane as shown above. If the equation y = -3 is graphed in the plane, how many points of intersection with the function f are there?

Solution :

Problem 18 :

In the system of equations above, k is a constant. If f(2) = -3, what is the value of k?

Solution :

Problem 19 :

A water pipe is in the shape of a circular tube. The figure above shows the pipe with a portion cut out. The dimensions of the pipe above are height 10 inches with thickness 4 inches. If the volume of the figure above is 800π cubic inches, what is the radius r of the inner circle in inches?

Solution :